Answer:
Step-by-step explanation:
The average rate of change of the function is represented by the following:
[tex]Average\ rate\ of\ change\ =\frac{Change\ in\ y\ }{Change\ in\ x\ }[/tex]
When we think about average rate of change of a function we actually need to calculate the slope of the line between the interval on the function in this case the function is f(x) = -3x^2 + 7x + 15 over the interval -2 ≤ x ≤ 2
in this case y = f(x) so here average rate of change is,
Average rate of change = Δf / Δx
so to calculate Δf we use the closed interval that is given [tex]-2\leq x\leq 2 \\[/tex]
so here goes,
[tex]f(x)=-3x^2+7x+15\\f(2)=-3(2)^2+7(2)+15\\f(2)=-12+14+15\\f(2)=17\\\\f(x)=-3x^2+7x+15\\f(-2)=-3(-2)^2+7(-2)+15\\f(-2)=-12-14+15\\f(-2)=-11\\[/tex]
so now , Δf = f(2) - f(-2) = final value of f(x) - initial value of f(x)
Δf = 17 - 11
Δf = 6 = Change in y
now we need Change in x which means Δx
so now,
Δx = final value of x - initial value of x
Δx = 2 - ( -2 )
Δx = 4
so now the Average rate of change = Δf / Δx
Average rate of change = 6/4
Average rate of change = 3/2
I have attached an image for you to visualize it clearly
